Question

Suppose Miss Roxanne Davenport is 25 years old right now and puts away $1,800 per quarter in an account that returns 6% interest.

If by the time she is 65 she has $1,179,415.39

b. [1 pt] What is her total contribution to the account? And how do I write the formula out?

c. How much interest did she earn?

Answer 1

Miss Roxanne is 25 years now and she will contribute 1800 per quarter till the age of 65 year. So, the contribution is made for 65-25 = 40 years.
Now, she contributes 1800 per quarter, so for 1 year it will be = 1800*4 = 7200
For 40 years it will be = 7200*40 =$288000

Total contribution = per quarter contribution*4*40
      1800*4*40
   = $288000
c) Total amount recieved at the end of 65 years at 6% interest = $1179415.39.
However, calculating the same through Future value annuity formula
Amount = [C*{(1+r/m)^m*n-1}]/ (r/m)
   where C = contribution made = 1800
   r = 6%
   m = compounding period = 4
   n = 40 years
Amount = [1800*{(1+0.06/4)^4*40-1}] / (0.06/4)
      = $1179415.39

Interest = Amount-Total payment
      = 1179415.39 - 288000

= $891415.39